Icosadodecahedron puzzle system

ABSTRACT

The IKOS holistic game of this invention comprises a semi-regular geometric solid of 32 faces. 12 faces are regular pentagons interfaced to 20 equilateral triangles. The polyhedron also comprises 60 equal upstand edges each one of which subtends 36 degrees at the centroid of the polyhedron. It also comprises 30 equal vertices at which four edges and four faces meet. The surface elements  1  of the IKOS are of seven distinct colors, with each surface element being of one color only. There are six sets of like colored surface elements with two pentagons and ten up-stands in each set. All the triangular panels are in the seventh, neutral, shade. Also included is a method of designing the 32&#39;dron on a CAD system.

RELATED DOCUMENT

[0001] This non-provisional application is a CIP (Continuation in Part) to non-provisional application Ser. No. 10/215,926 filed Aug. 2, 2002 which in turn was based upon provisional application Ser. No. 60/311,242 filed Aug. 10, 2001 by the same inventor with the same title and which was filed within one year and the applicant claimed priority there from.

BACKGROUND

[0002] This invention relates generally to games. More particularly it relates to a puzzle based on a regular multi-colored Icosadodecahedron which totally involves and benefits the mind and spirit of children and adults alike. An embodiment of the puzzle is also known by it's trademark name of IKOS for all products based on this invention.

THE PROBLEM

[0003] The problem with prior art games and puzzles is that they can either be played indoors or outdoors but not both. Likewise they can either be enjoyed by children or adults but not both. Prior art puzzles are not holistic as they do not involve and benefit body mind and spirit of children and adults both indoor and outdoors. Problems with prior games and puzzles and toys can be categorized into the following:

[0004] a) Useable only indoors or outdoors but not both

[0005] b) Challenging to children or adults but not both

[0006] c) Provide benefits for the body or mind but not spirit.

[0007] d) Not cost effective.

[0008] e) Do not harmonize with the environment.

[0009] f) Do not totally engage or involve the players.

[0010] g) Educational or entertaining but seldom both.

SUMMARY

[0011] The IKOS holistic puzzle of this invention comprises comprises a semi-regular geometric solid of 32 faces. 12 faces are regular pentagons interfaced to 20 equilateral triangles. The polyhedron also comprises 60 equal upstand edges each one of which subtends 36 degrees at the centroid of the polyhedron. It also comprises 30 equal vertices at which four edges and four faces meet.

[0012] The surface elements 1 of the IKOS are of seven distinct colors, with each surface element being of one color only. There are six sets of like colored surface elements with two pentagons and ten up-stands in each set. All the triangular panels are in the seventh, neutral, shade.

[0013] This indoor-outdoor puzzle and game appeals equally to children, teens and adults. It can played anywhere! This versatile bundle of fun is the perfect combination of fun and education for all situations! The possibilities for this active game are limitless.

[0014] All of this isn't just fun play. Players develop mental thinking skills, visual perceptual skills, and spatial relationships. As kids explore the world of shapes, patterns and colors, they begin to develop color recognition, memory and beginning geometry skills. Players also improve key skills like visual discrimination, and problem solving. This game promotes creative play and socialization.

[0015] It also encourages more family interactions. Parents or educators can use the IKOS to teach younger children how to recognize different kinds of shapes, colors or identify images such as different kinds of animals to name a few.

[0016] The game is ideal for developing better health, keen mind and strong spirit as well as team spirit among players and family bond and unity, which in turn has positive impact on society by reduced juvenile delinquency and crime.

PRIOR ART

[0017] A preliminary limited prior art search was conducted. Furthermore the inventor is intimately familiar with the prior art. Following are typical examples of the prior art known to the applicant arranged in the reverse chronological order for ready reference of the reader.

[0018] h) U.S. Utility Pat. No. 6,398,221 earned by the applicant John Alexander Graham on Jun. 4, 2002 for “Polyhedron Globe Puzzle System”

[0019] g) U.S. Utility Pat. No. 5,236,196 awarded to Blankenburg et al on Aug. 17, 1993 for “Spherical Body Formed of Polygonal Members”

[0020] f) U.S. Utility Pat. No. 4,781,380 presented to Thomas J. Irwin on Nov. 1, 1988 for “Articulated Ring Puzzle”

[0021] e) U.S. Utility Pat. No. 4,529,201 bestowed upon Ernest Nadel on Jul. 16, 1985 for “Multi-Faceted Solid Geometrical Puzzle Toy”

[0022] d) U.S. Utility Pat. No. 4,478,418 issued to Benjamin F. Sherman Jr. on Oct. 23, 1984 for “Three-Dimensional Sliding Element Puzzle”

[0023] c) U.S. Utility Pat. No. 4,474,376 presented to William Gustafson on Oct. 2, 1984 for “Manipulable Icosahedron Toy”

[0024] b) European Patent Application 82304147.0 published on 16 Feb. 1983 No. 0072215 entitled Improved Puzzle by Christopher John Walton

[0025] a) PCT application PCT/HU82/00017 entitled “A Logical Toy Having Movable Units as Compared to Each Other and to the Core” by Szlivka & Gyoengyoesi published as publication number WO82/03564 on 28 Oct. 1982.

[0026] None of the prior art devices known to the applicant or his attorney disclose the EXACT embodiment of this inventor that constitutes a simple, elegant, quick, convenient, affordable, educational, engaging, challenging and entertaining puzzle for children and adults alike.

OBJECTIVES

[0027] Unfortunately none of the prior art devices singly or even in combination provide for all of the objectives as established by the inventor for this system as enumerated below.

[0028] 1. It is an objective of this invention to provide methods, devices and system for playing a holistic puzzle.

[0029] 2. Another objective of this invention is to provide a puzzle that involves engages and challenges both children and adults.

[0030] 3. Another objective of this game is that it be suitable for using and playing indoors as well as out doors.

[0031] 4. Another objective of this game is that it be both educational and entertaining.

[0032] 5. Another objective of this game is that it be aesthetic and elegant design that integrates harmoniously with any environment.

[0033] 6. Another objective of this IKOS is that it can be used as decoration to accent surrounding objects at home or office.

[0034] 7. Another objective of this puzzle is that it be holistic to engage not only mind but also develop motor skills.

[0035] 8. Another objective of this puzzle is that its use is quick, simple, convenient and easy.

[0036] 9. Another objective of this invention is that it be suitable for all types of users in all types of conditions.

[0037] 10. Another objective of this invention is that the puzzle be portable.

[0038] 11. Another objective of this invention is that its design is simple and even elegant.

[0039] 12. Another objective of this invention is that its use is intuitive which requires no further training.

[0040] 13. Another objective of the game of this invention is that it be capable of multiple uses.

[0041] 14. Another objective of this invention is that it use little or no additional energy.

[0042] 15. Another objective of this invention is that the invention use modular standard components easily interface-able transportable and storable.

[0043] 16. Another objective of this invention is that it be reliable such that it practically never fails and requires little or no maintenance.

[0044] 17. Another objective of this invention is that it be environmentally friendly and use biodegrade materials to the extent practical.

[0045] 18. Another objective of this invention is that it be physically safe in normal environment as well as accidental situations.

[0046] 19. Another objective of this invention is that it be long lasting made from durable material.

[0047] 20. Another objective of this invention is that it meet all federal, state, local and other private standards guidelines, regulations and recommendations with respect to safety, environment, energy consumption.

[0048] 21. Another objective of this invention is that it not compromise the safety or the comfort of the players.

[0049] 22. Another objective of this invention is that it be suitable for gift giving.

[0050] 23. Another objective of this invention is that it be suitable for promotional give-aways complete with message of the sponsor such as a union, casino or charitable organization.

[0051] 24. Another objective of this invention is that it promote family unity and family bond as well as team spirit, unity and bond among unrelated players.

[0052] 25. Another objective of this invention is that the game not only be entertaining but capable of learning and teaching.

[0053] 26. Another objective of this educational game is to provide a CAD (Computer Aided Design) embodiment.

[0054] Other objectives of this invention reside in its simplicity, elegance of design, ease of manufacture, service and use and even aesthetics as will become apparent from the following brief description of the drawings and the detailed description of the concept embodiment.

[0055] Unfortunately none of the prior art devices singly or even in combination provide all of the features established by the inventor for this system as enumerated below.

[0056] a) Educational, engaging, challenging and entertaining.

[0057] b) Safe and holistic.

[0058] c) Multiple uses for all types of players and all types of venues.

[0059] d) A device that can be easily used, stored, and maintained.

BRIEF DESCRIPTION OF THE DRAWINGS

[0060] a) FIG. 1 shows a plan view of the regular icosadodecahedron.

[0061] b) FIG. 2 shows plan view of the IKOS in schematic geometric form which is a pseudo perspective isometric plan view.

[0062] c) FIG. 3 shows the rotational path of a colored pentagonal floret in a pseudo perspective isometric plan view of the icosadodecahedron

[0063] d) FIG. 4 shows the rotational path if a triangular floret in a pseudo perspective isometric plan view of the icosadodecahedron

[0064] e) FIG. 5 shows rotational path about its axis of a hemisphere of the icosadodecahedron in pseudo perspective isometric plan view.

[0065] f) FIG. 6 shows uniformly colored pentagonal florets arranged as polar opposites in a pseudo perspective isometric plan view of the icosadodecahedron.

[0066] g) FIG. 7 shows like colored pentagonal florets adjacent and in the ‘cubic’ arrangement in a pseudo perspective isometric plan view of the icosadodecahedron

[0067] h) FIG. 8 shows opposite pentagonal panels and corresponding equator all of the same color in a pseudo perspective isometric plan view of the icosadodecahedron

[0068] i) FIG. 9 shows pentagonal panels of the same color adjacent and enclosed within a crescent of like colored up-stands in a pseudo perspective isometric plan view of the icosadodecahedron.

[0069] j) FIG. 10 shows colored surface elements in a random arrangement in a pseudo perspective isometric plan view of the icosadodecahedron.

[0070] k) FIG. 11 shows pentagonal panel substructure and superstructure as a CAD embodiment.

[0071] l) FIG. 12 shows triangular panel substructure and superstructure as a CAD embodiment.

[0072] m) FIG. 13 shows upstand edge substructure and superstructure and the alignment between them as a CAD embodiment.

[0073] n) FIG. 14 shows upstand edge substructure alignment with superstructure as a CAD embodiment of FIG. 13 in greater detail.

DETAILED DESCRIPTION OF THE BEST MODE PREFERRED EMBODIMENT

[0074] As shown in the drawings wherein like numerals represent like parts throughout the several views, there is generally disclosed in FIG. 1 a plan view of the regular icosadodecahedron 100. FIG. 2 shows plan view of the IKOS in schematic geometric form which is a pseudo perspective isometric plan view.

[0075] The IKOS is in the shape of a regular icosadodecahedron 100, hence the name. This is a semi-regular geometric solid of 32 faces 1, see Diagram 1. Twelve of the faces are regular pentagons 5 and twenty are equilateral triangles 3.

[0076] The faces are so disposed that polygons of one type are laterally adjacent at all edges 2 to polygons of the other type, while polygons of the same type are invariably vertically adjacent.

[0077] This polyhedron has 60 equal edges 2, each one of which subtends 36 degrees at the centroid of the polyhedron, and 30 equal vertices 6, at which four edges and four faces meet.

[0078] An important property of the icosadodecahedron, (32'dron), is that the 60 edges 2 form themselves into six mutually equiangular, mutually intersecting, regular decagons 7, each one of which bisects the 32'dron exactly.

[0079] In the IKOS 100 the edges 2 are made to stand proud of the faces to form equal up-stand 2. The outer edges of these up-stand 2 together form the skeleton of a projected, larger, concentric 32'dron defined only by its edges 2.

[0080] Four up-stands 2, meet at a projected vertex 6. The end edges of the up-stand 2 meet along the outermost section of the radial line from the centroid of the figure to the outer vertex 6. The up-stands form themselves, correspondingly, into 6 equivalent hollow decagons. The 60 up stand edges 2 and the 32 polygonal panels 3,5 are referred to as the surface elements or faces 1 of the IKOS 100.

[0081] The surface elements 1 of the IKOS are of seven distinct colors, with each surface element being of one color only. There are six sets of like colored surface elements with two pentagons and ten up-stands in each set. All the triangular panels are in the seventh, neutral, shade. The color legend for the embodiment delineated here is as follows. 10 = Color 1 (Yellow) 20 = Color 2 (Red) 30 = Color 3 (Green) 40 = Color 4 (Blue) 50 = Color 5 (Purple) 60 = Color 6 (Orange) 70 = Color 7 (Silver or neutral) color

[0082] In the IKOS all the surface elements 1 can be made to move, i.e. rotate in clusters, relative to each other and to the core of the device. The geometric structure of the IKOS 100 remains unchanged after any number of movements. Furthermore, irrespective of the number of moves that are made, an up-stand 2 always has polygons of one type lying on one side of it.

[0083] The object of the puzzle is to achieve a desired patterning of the colored surface elements through successive rotations of different element clusters.

[0084] There are three possible types of movement in the IKOS. FIG. 3 shows the rotational path of a colored pentagonal floret in a pseudo perspective isometric plan view of the icosadodecahedron. FIG. 4 shows the rotational path if a triangular floret in a pseudo perspective isometric plan view of the icosadodecahedron FIG. 5 shows rotational path about its axis of a hemisphere of the icosadodecahedron in pseudo perspective isometric plan view.

[0085] a) Rotation, about its center, of a pentagonal floret 111, as shown in FIG. 3 wherein a Floret is taken to mean the combination of any polygonal panel and its three, or five, surrounding up-stands. This rotation can be made in either sense and there are four possible new orientations the floret can move into.

[0086] b) Rotation, about its center, of a triangular floret 112, as shown in FIG. 4. This rotation can be made in either sense and there are two possible new orientations the floret can move into.

[0087] c) Rotation of one hemisphere 113 relative to the other, as shown in FIG. 5. Rotation can be made in either sense and there are four possible new orientations the hemisphere can assume. In this movement the up stand decagon 7 dividing the two hemispheres is called the equatorial decagon and the surface elements immediately adjacent to it are referred to as being equatorially adjacent. The axis of rotation invariably passes through the centers of a pair of opposite pentagonal florets 4P, referred to as the polar florets, with the surface elements adjacent to it referred to as being polar adjacent.

[0088] In this rotation the equatorial decagon 7 remains stationary, so that a total of 41 surface elements are rotated relative to the rest. There is no one solution to the puzzle. There are a number of generic solutions, and associated with each one of these are usually about 12 specific solutions, depending on the number of different color arrangements that are possible in any one generic solution. FIG. 6 shows uniformly colored pentagonal florets arranged as polar opposites in a pseudo perspective isometric plan view of the icosadodecahedron.

[0089]FIG. 7 shows like colored pentagonal florets adjacent and in the cubic arrangement in a pseudo perspective isometric plan view of the icosadodecahedron

[0090] There are two broad types of generic solutions: those in which the pentagonal florets 4P are of a uniform color, type A, and those in which the up stand decagons, or segments of them, are of a uniform color, type B.

[0091] Type A generic solutions include those where:

[0092] a) Like colored pentagonal florets 4P are disposed as polar opposites, see Diagram 6.

[0093] b) Like colored florets are adjacent i. e. sharing a common vertex, including, in particular, where the 6 common vertices correspond to the centers of faces of a concentric cube, i.e. the ‘cubic’ arrangement, see Diagram 7.

[0094] c) They are neither polar opposites nor adjacent.

[0095] d) Hybrids of any of the above.

[0096]FIG. 8 shows opposite pentagonal panels and corresponding equator all of the same color in a pseudo perspective isometric plan view of the icosadodecahedron. FIG. 9 shows pentagonal panels of the same color adjacent and enclosed within a crescent of like colored up-stands in a pseudo perspective isometric plan view of the icosadodecahedron.

[0097] Type B generic solutions include those where:

[0098] a) Like colored pentagonal panels 5 are arranged as polar opposites with the correspondingly colored upstand 2 decagons forming the respective equators. In this arrangement all like colored elements lie in parallel planes, as shown in FIG. 8.

[0099] b) Like colored panels are adjacent and in the ‘cubic’ arrangement, with correspondingly colored up-stand 2 enclosing them in a crescent made up of two half-decagons as shown in FIG. 9.

[0100] There are innumerable other regular and semi-regular patterns, which may be regarded as solutions to the puzzle, but these are too numerous to mention here.

[0101] Although the number of patterns that could be regarded as solutions to the puzzle runs into hundreds, the number of random arrangements is so vast as to make it virtually impossible to arrive through a random sequence of movements.

[0102]FIG. 10 shows the IKOS 100 with the colored surface elements in a random arrangement in a pseudo perspective isometric plan view of the icosadodecahedron. The puzzle is played by participants from age 3 to adults of all ages. It can be used indoors as well as outdoors. The game is also known by its potential trademark name of “IKOS”. The objective of the puzzle like the Rubik's cube is to put the IKOS in like colors from a random order in the shortest time. The object of the puzzle is to achieve a desired patterning of the colored surface elements through successive rotations of different element clusters.

[0103] The manufacturing, assembly and use of this invention is very simple even intuitive. The drawings delineate this process even further wherein FIG. 11 shows pentagonal panel substructure 105 and superstructure 195 as a CAD embodiment complete with pentagonal shaft 115 over base 115 of pentagonal shaft on underside of the panel.

[0104]FIG. 12 shows triangular panel substructure 103 and superstructure 193 as a CAD embodiment complete with circular shoe 120 which is a segment of hollow sphere that engages with spherical core, spacer 130 as seen through the panel tetrahedronal shaft 134 and base 135 of tentrahedronal shaft in the plane of the inner face of the spacer 130.

[0105]FIG. 13 shows upstand edge substructure 102 and superstructure 192 and the alignment 155 between them as a CAD embodiment complete with shaft 150 and virtual hollow shaft 151, smaller trapezium 160, larger trapezium 170, and the interface 165 between trapezia small 160 and large 170.

[0106]FIG. 14 shows upstand edge substructure 102 alignment 155 with superstructure 192 shaft 150 and alignment 155 as a CAD embodiment of FIG. 13 in greater detail. The interconnection between elements can be anything as long as does not interfere with the rotational aspects of the puzzle.

Method of Construction the IKOS on CAD

[0107] There are 5 stages to this operation:

[0108] I. Creating the geometric foundation to the Ikos

[0109] II. Constructing the spherical core.

[0110] III. Constructing the 12 pentagonal panels

[0111] IV. Constructing the 20 triangular panels

[0112] V. Constructing the 60 Upstand Edges

[0113] A description and method steps for each follow.

[0114] I. Create the geometrical Foundation of the IKOS

[0115] a) To create an icosadodecahedron OF FIG. 1 (hereinafter referred to as a 32'dron).

[0116] i) Draw a regular decagon of side 30 mm.

[0117] ii) Draw a similar decagon sharing a diagonal with the first.

[0118] iii) Rotate the plane of the second decagon about the common diagonal, by an angle of 58.283 degrees, which is [ Tan inverse (Sq Rt 5+1)/2]

[0119] iv) Repeat this about the remaining four diagonals of the first decagon.

[0120] Select a neighboring diagonal, draw a decagon as before, but then rotate in the opposite sense. Continue by alternating the sense with successive diagonals. The result should be the-figure whose half-view is shown in FIG. 1.

[0121] v) Fill in the plane faces, 12 pentagonal and 20 triangular, of the resultant 32'dron. This FIG. 1 is referred to below as the primary 32'dron. Its 3-D center is referred to as the centroid.

[0122] b) To create a secondary concentric 32'dron, use edge length of 48.541 mm, ie. 30×(Sq Rt5+1)/2. Leave this as a wire frame.

[0123] c) Create a hollow concentric sphere, outer radius 23 mm and 3 mm in thickness.

[0124] II. Construct the Core to the 32'dron.

[0125] a) Construct a sphere, radius 20 mm, center at the centroid. This is the base over which the polygonal panels rotate and move. It is immediately inside the hollow concentric sphere just created in step I supra.

[0126] What follows are instructions for making, in-situ, a single specimen for each generic component of the Ikos. A complete or partial assembly can then be built up by copying. The intention is to be able to show the object in its entirety, as viewed from the outside and to show the full section through the Centroid, as well as views of the individual parts, singly and in clusters, and how they relate to the whole. Construction of the polygonal panels is best done on a pair of adjoining faces. The upstand edge is then constructed on the common edge.

[0127] The terms ‘inner’ and ‘outer’ refer respectively to towards and away from the centroid. The terms superstructure and substructure refer respectively to the outer visible surface and the inner parts of the completed Ikos.

[0128] III. Construct the Pentagonal Panel (1 of 12 No), Superstructure and Substructure.

[0129] a) To construct the superstructure.

[0130] i) On a pentagonal face of the prime 32'dron draw a smaller parallel and concentric regular pentagon of side length 27.649 mm. This is the geometric base of the pentagonal panel.

[0131] ii) Construct the panel. Thickness is 1.5 mm, with outer surface 0.5 mm out from the pentagonal base. Edges of panel are perpendicular to the surfaces.

[0132] b) The substructure 105 comprises a pentagonal pyramidal shaft 115 and a circular shoe 120 that engages with the surface of the spherical core.

[0133] To construct the substructure

[0134] i) On the inner side of the panel just constructed draw a smaller parallel concentric regular pentagon of side length 22.959 mm, This is the geometric basis of the substructure.

[0135] ii) Construct a pentagonal pyramid with its apex at the centroid, and its base on the pentagon just drawn.

[0136] iii) Eliminate the peak of the pyramid lying within the 23 mm sphere.

[0137] c) To construct the circular shoe.

[0138] i) On the pentagonal face, above, of the prime 32'dron draw the in-circle and, with this as a base, create a cone with its apex at the centroid. This is the geometric basis to the shoe.

[0139] ii) Construct the shoe 120 by eliminating all of the cone that lies outside and inside the spherical shell.

[0140] The resultant composite figure is the pentagonal panel, substructure and superstructures shown in perspective in Diagram 11, non in-situ.

[0141] IV. Construct the Triangular Panel (1 of 20 No), Superstructure and Substructure.

[0142] a) To construct the triangular panel superstructure 193.

[0143] i) On a triangular face, adjacent to the pentagonal selected above, draw a smaller concentric parallel equilateral triangle of side length 25.546 mm.

[0144] ii) Construct a panel 1 mm thick on the triangle just drawn, with the outer surface of the panel 0.5 mm out from the triangle.

[0145] b) The substructure comprises a spacer 130, a tetrahedronal shaft and a circular inner shoe 120 that engages with the surface of the spherical core.

[0146] To Construct the substructure 103.

[0147] i) Construct the spacer 130. Inscribe on the inner surface at the panel just constructed a line of length 7.374 mm. One end of this line is at the center of the triangle.

[0148] ii) Draw a rectangle 1.827 mm wide, and inwards from this line. The plane of this rectangle is perpendicular to the plane of the triangular surface.

[0149] iii) Trim off the corner of the rectangle diagonally opposite the center of the triangle. The trimming point is at a distance of 0.951 mm from the surface, along the shorter side and the angle of trim is 74.247 degrees to the shorter side.

[0150] iv) Construct the spacer 130 by rotating this trimmed off rectangle a full revolution about the side that lies along the normal from the centroid to the center of the triangle. The inner face of the spacer should be a circle of radius 4.268 mm.

[0151] c) Construct the tetrahedronal shaft 135.

[0152] i) The base of the shaft 135 is an equilateral triangle, sides parallel with the panel, and drawn in the plane of the inner surface of the spacer just constructed.

[0153] Side length of triangle is 14.786 mm and apex of the tetrahedron is at the centroid.

[0154] ii) Construct the shaft 135 by eliminating the peak that lies within the 23 mm radius sphere. It should be noted that the base vertices of the shaft overlap the spacer.

[0155] d) Construct the circular inner shoe 120.

[0156] i) Draw the geometric basis of the inner shoe. This is a cone whose base is the in-circle of the triangular face of the prime 32'dron and whose apex is at the centroid.

[0157] ii) Construct the inner shoe by eliminating the parts of the cane that lie outside and inside the 3 mm zone of the spherical shell (outer radius 23 mm). The completed figure should be as shown in FIG. 12.

[0158] e) Eliminate alt of the spherical shell that lies outside the circular shoes to both types of panel.

[0159] V Construct an Upstand Edge, (1 of 60 No), Substructure and Superstructure

[0160] a) The geometric foundation to the substructure 102 is the common volume to two intersecting but different double cones. These are formed on each face, pentagonal and triangular, to the prime 32'dron. To construct the geometric foundation.

[0161] i) Create 2 double cones, one to each plane face of an adjoining pentagon and triangle of the prime 32⁴dron. The common bases of the double cones are the circumcircles-to the respective polygons.

[0162] There is therefore an inner and an outer cone for each. There is also some non-coplanar interpenetration at the common bases.

[0163] ii) The apex of each inner cone is at the centroid.

[0164] iii) The base angle of the inner cone to the pentagonal face is 58.283°.

[0165] iv) The base angle of the outer cone to the pentagonal face is 53.1300 (tan -¹4/3).

[0166] v) The base angle of the inner cone to a triangular face is 74.O35°

[0167] vi) The base angle of the outer cone to a triangular face is 37.377 degrees

[0168] The double cones are seen to interpenetrate. The two vertical axes meet at the centroid at an angle of 37.377 degrees. The common volume figure corresponds to the common edge between the two faces of the prime 32'dron.

[0169] b) Eliminate the double cones except for the common volume figure.

[0170] c) Eliminate the part of the common volume that- lies within the 23 mm radius sphere.

[0171] d) Trim the end edges of the shape thus formed. This operation may be carried out in the following way which assumes that the pentagonal and triangular panels have been constructed on adjacent faces of the prime 32'dron, and the upstand is being constructed on the common edge. In the substructure shafts, see 2b) and 3c) supra, there are two pairs of coplanar faces, two face types to each pair.

[0172] i) Create two planes to join the faces within each pair. The two planes are seen to cut across the respective end edges of the shape just formed. (They meet along the triangular shaft edge that lies opposite the-common edge between the two polygons.)

[0173] ii) Trim, by cutting off the end edges of the shape that protrude through the planes on either side.

[0174] e) Create a shaft, outward from the shape, and along the central normal axis. (The central normal axis lies in the radius from the centroid).

[0175] i) The shaft is 5 mm long

[0176] ii) The shaft is elliptical in cross section. The long ads lies parallel to the edge of the 32'dron and is 2 mm long. The short axis is 1 mm.

[0177] The resultant shape is as illustrated in perspective, non in-situ, in FIGS. 13 & 14

[0178] e) Create the upstand edge superstructure. The form of the upstand edge superstructure is generated by two different hut regular trapezia whose planes intersect at right angles.

[0179] i) Create the larger trapezium. The plane of this passes through the centroid.

[0180] ii) The larger, outer side is an edge of the secondary 32'dron, length 48.541 mm.

[0181] iii) the shorter, inner side is 18.500 mm in length, at a perpendicular distance of 29.650 mm.

[0182] iv) The non-parallel opposite sides are each at an angle of 63.1330 to the longer side.

[0183] f) Create the smaller trapezium. This plane of this intersects at right angles, the plane of the larger trapezium.

[0184] i) Create the smaller trapezium to intersect the larger at a distance of 2.127 mm from the larger's inner side. This line of intersection lies parallel to the two parallel sides of the larger trapezium and is parallel to, and midway between, the parallel sides of the smaller trapezium.

[0185] ii) The larger side of the smaller trapezium is 25.127 mm and is aspected towards the pentagonal face.

[0186] iii) The smaller side is 16.182 mm long and is aspected towards the triangular face.

[0187] iv) The distance between the two sides is 8.570 mm.

[0188] v) The non-parallel side is at an angle of 62.268° to the longer parallel side.

[0189] This is the geometric basis of the upstand superstructure and is outlined in FIG. 11.

[0190] g) To construct the-upstand superstructure.

[0191] i) Connect each end of the outer side of the larger trapezium to the corresponding ends of the longer and shorter sides of the smaller, then connect these two points to the corresponding ends of the inner side of the larger trapezium.

[0192] The result should be a solid figure of six faces, two larger trapezia and two smaller trapezia, neither pair identical, with two irregular but symmetrical quadrilaterals at each end. This figure is symmetrical about the plane through the centroid and the centers of the relevant pentagon and triangle of the prime 32'dron.

[0193] In having eight nodes, twelve edges (four of them parallel) and six quadrilateral faces, it may also he viewed as a mutated cube.

[0194] ii) Construct a hollow shaft to receive the solid shaft from the substructure. At the mid-point of the innermost edge of the figure, and along the normal from the centroid, construct an opening shaft 5 mm long and elliptical in cross section with the major axis (diameter) of the ellipse 4 mm in length and parallel to the parallel edges of the figure, and the minor axis 2 mm in length (within the plane of symmetry referred to above).The resultant figure, non in-situ, is as shown in diagram 14. Both the sub- and superstructure figures should fit together in proper alignment on CAD

[0195] The inventor has given a non-limiting description of the drop case rapid weapon deployment system of this invention. Due to the simplicity and elegance of the design of this invention designing around it is very difficult if not impossible.

[0196] Nonetheless many changes may be made to this design without deviating from the spirit of this invention. Examples of such contemplated variations include the following:

[0197] 1. The shape and size and quantity of the various members and components may be modified.

[0198] 2. The color, aesthetics and materials may be enhanced or varied.

[0199] 3. A different educational graphic may be selected for learning and teaching different substantive subjects through this medium of instruction.

[0200] 4. Additional complimentary and complementary functions and features may be added.

[0201] 5. A more economical version of the puzzle may be adapted.

[0202] 6. An audio-visual computer version of the game may be employed.

[0203] 7. In lieu of or in addition to elements may be embossed or studded to enhance the tactile-spatial awareness of the user.

[0204] Thus this puzzle is not limited to the exact embodiment shown. The shapes can be substituted for colors, numbers, letters, animal figures, images, patterns and more.

[0205] It can have a version where it is played in the swimming pool and at night where glow in the dark material or other illuminating devices are used. This game can also have a software program version where the user can have the ability to customize the images to be used on the game.

[0206] Other changes such as aesthetics and substitution of newer materials as they become available, which substantially perform the same function in substantially the same manner with substantially the same result without deviating from the spirit of the invention may be made.

[0207] Following is a listing of the components used in the best mode preferred embodiment arranged in ascending order for ready reference of the reader.  1 = Faces  2 = Edges or up-stands  3 = Triangles  4 = Floret  5 = Pentagons  6 = Vertices  7 = Decagon  8 = Hemisphere  9 = Axis of rotation  10 = Color 1 (Yellow)  13 = Yellow Triangle  15 = Yellow Pentagon  20 = Color 2 (Red)  23 = Red Triangle  25 = Red pentagon  30 = Color 3 (Green)  33 = Green Triangle  35 = Green Pentagon  40 = Color 4 (Blue)  43 = Blue Triangle  45 = Blue Pentagon  50 = Color 5 (Purple)  53 = Purple Triangle  55 = Purple Pentagon  60 = Color 6 (Orange)  63 = Orange Triangle  65 = Orange Pentagon  70 = Color 7 (Silver or neutral) color  73 = Silver Triangle  80 = Multi-Color 100 = IKOS puzzle generally 102 = Upstand edge substructure 103 = Triangular panel substructure 105 = Pentagonal panel substructure 110 = Rotational movement 111 = Rotational movement of a pentagonal floret about its center 112 = Rotational movement of triangular floret about its center 113 = Rotation of the two hemispheres with respect to each other 115 = Pentagonal shaft 116 = Base of Pentagonal shaft on underside of panel 120 = Circular shoe (segment of hollow sphere that engages with spherical core 130 = Spacer as seen through the triangular panel 134 = Tetrahedronal shaft 135 = Base of tetrahedronal shaft in plane of inner face of spacer 150 = Upstand edge shaft 151 = Hollow virtual shaft 155 = Alignment vector 160 = Extent of smaller trapezium 165 = Trapezia intersectional interface line 170 = Extent of larger trapezium 175 = Segments of common bases to double cones 180 = Edge of 32'dron 192 = Upstand edge superstructure 193 = Triangular panel superstructure 195 = Pentagonal panel superstructure

DEFINITIONS AND ACRONYMS

[0208] A great care has been taken to use words with their conventional dictionary definitions. Following definitions are included here for clarification. 3D = Three Dimensional CAD = Computer Aided Design DIY = Do It Yourself Floret = Polygonal panel and its three, or five, surrounding up-stands. Integrated = Combination of two entities to act like one Interface = Junction between two dissimilar entities OEM = Original Equipment Manufacturer

[0209] While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments as well as other embodiments of the invention will be apparent to a person of average skill in the art upon reference to this description. It is therefore contemplated that the appended claim(s) cover any such modifications, embodiments as fall within the true scope of this invention. 

The inventor claims:
 1. An icosadodecahedron puzzle system comprising 12 pentagons symmetrically and geometrically and rotationally interfaced to 20 equilateral triangles and 60 upstand edges resulting in two hemispheres each with plurality of pentagonal florets and triangular florets.
 2. The icosadodecahedron puzzle system of claim 1 wherein; a) said pentagons are regular and identical shape; and b) said 60 upstand edges are all equal.
 3. The icosadodecahedron puzzle system of claim 1 wherein; a) each one of said edges subtends 30 degrees at the centroid of said icosadodecahedron; and b) said icosadodecahedron further having 30 equal vertices.
 4. The icosadodecahedron puzzle system of claim 3 wherein at each of said 30 equal vertices 4 of said 60 equal edges and four of said 32 faces meet.
 5. An polyhedron puzzle system comprising 12 pentagons symmetrically and geometrically and rotationally interfaced to 20 equilateral triangles and 60 upstand edges resulting in two hemispheres each with plurality of pentagonal florets and triangular florets.
 6. The polyhedron puzzle system of claim 5 which is an icosadodecahedron puzzle with 32 sides.
 7. The polyhedron puzzle system of claim 6 wherein; a) said pentagons are regular and identical shape; and b) said 60 upstand edges are all equal.
 8. The polyhedron puzzle system of claim 7 wherein; a) each one of said edges subtends 30 degrees at the centroid of said icosadodecahedron; and b) said icosadodecahedron further has 30 equal vertices.
 9. The polyhedron puzzle system of claim 8 wherein at each of said 30 equal vertices four of said 60 equal edges meet.
 10. The polyhedron puzzle system of claim 8 wherein at each of said 30 equal vertices four of said 32 faces meet.
 11. A polyhedron of 32 faces of 12 regular pentagons and 20 equilateral triangles having 60 equal edges rotationally interconnected symmetrically and geometrically resulting in two hemispheres each with plurality of pentagonal florets and triangular florets wherein each one of said edges subtends 30 degrees at the centroid of said polyhedron and said polyhedron further having 30 equal vertices wherein at each of said 30 equal vertices 4 of said 60 equal edges and four of said 32 faces meet. 